Answer

Since the number leaves the remainder 9 and 7 when divides 285 and 1249 respectively.

⇒ number completely divides 285 – 9 = 276 and 1249 – 7 = 1242

And greatest of that number will be HCF(276, 1242)

Now, 1242 = 276 × 4 + 138

276 138 × 2 + 0

So, HCF(276, 1242) = 138 and that is required number.

OR

Composite numbers are those numbers which have a factor other than 1 and itself.

For example: 28 is a composite number as 28 = 2 × 2 × 7 and has factors other than 1 and 28.

Now,

(7 × 11 × 13 + 13)

= 13(7 × 11 + 1)

= 13 × 78

Since this number has two factors other than 1 and itself it is a composite number.

And

(7×6×5×4×3×2×1 + 5)

= 5(7 × 6 × 4 × 3 × 2 + 5)

= 5(1008 + 5)

= 5 × 1013